Seems like a lot of different audiences. My observation is this is trying to cover 2 of the 3 common tracks:

1 - Proof based calculus for math majors

2 - Technique based calculus for hard science majors

3 - Watered down calculus for soft science and business majors (yes, there are a few schools that are exceptions to this)

If he can pull off unifying 1 and 2, good for him!

I don't think they are unifiable, the aims and methods one needs to learn are just too different. Limits of covering boxes and scaling your epsilons and so on, stuff from Tao's class on analysis is far away from being able to deal either non-trivial differential equations or stability analysis. You can prove all sorts of things about dense subspaces of Hilbert space and still get totally lost in multiple scale analysis, and vice versa. (Ed: epsilon was spelled espikon)